The dispersion coefficient of displacing fluids within porous media is an important parameter to measure accurately for a range of applications. For example, enhanced gas recovery is an emerging technology where carbon dioxide is injected into natural gas reservoirs as a means of maintaining the pressure of the reservoir and to hence enhance the natural gas recovery, with the additional benefit of carbon dioxide sequestration. Research is currently being done to measure the dispersion coefficient of carbon dioxide into methane because carbon dioxide is a contaminant that reduces the value of the natural gas. Such dispersion experiments are difficult to perform in the laboratory using conventional rock core flooding equipment as erroneous contributions to the dispersion process from entry and exit effects (into and out of the rock core respectively) are impossible to eliminate completely. Previously, we have estimated the resultant error to be of the order of 25 % (Hughes et al., Int J Greenh Gas Control 9:457-468, 2012). Here we effectively deploy spatially resolved breakthrough curves which are characteristic of the dispersion process for carbon dioxide replacing methane. These are obtained from time-resolved 1D magnetic resonance imaging (MRI) profiles. By analysis of the additional dispersion between these time-resolved profiles, we are able to eliminate the entry/exit effects and obtain more accurate values for the dispersion coefficient. We demonstrate this using a model porous medium (mono-dispersed glass beads) in a cell capable of holding gas pressures up to 80 bar in a low-field MRI rock core analyser. Via simultaneous conventional IR analysis of the carbon dioxide effluent to determine the dispersion coefficient, we are also able to directly quantify the magnitude of the error due to these entry/exit effects.